If we, as students, stay at the teacher's feet for the duration of our lives we risk becoming clones. If we look, really look, we will see that the teacher's approach is always a bit different from his/her teacher, who was in turn different from the preceding teaching, etc... Perhaps the ultimate points are the same, but the approach, the form, the constituent ingredients are fresh and innovative. That is the hallmark of a living teaching. At the same time, we are typically indebted to and connected with our teacher(s). That is also a hallmark of a living teaching.
Venturing out has a thousand faces. There is no one way to do that. Many teach in turn. Others just apply and live. There is no template for that, and that is a big reason why it isn't easy. We may also find that we are , in many ways, right back where we were when we began, albeit with more tools and experience. We may find that leaving the teacher brings us back to the world that we inhabited before. This is one of the first real tests of the teaching. The world we left has always been here in our presence. Hopefully we can experience it through various lenses.
It may be the case that one needs to completely move on, leaving the teaching and the teacher behind. If so, we hope the teaching itself was solid enough to support the new reality. In many cases, however, we don't turn our backs on the teaching or the teacher; we do move on but we stay engaged with teacher and teaching as well, forging a new now while respecting the past. Either way, we find ourselves in a brave new world, so to speak. There is no going back. Forget about it. There is only forward. Would that we all walk it well.